Bayesian parameter uncertainty modeling in a macroscale hydrologic model and its impact on Indian river basin hydrology under climate change

Macroscale hydrologic models (MHMs) were developed to study changes in land surface hydrology due to changing climate over large domains, such as continents or large river basins. However, there are many sources of uncertainty introduced in MHM hydrological simulation, such as model structure error, ineffective model parameters, and low‐accuracy model input or validation data. It is hence important to model the uncertainty arising in projection results from an MHM. The objective of this study is to present a Bayesian statistical inference framework for parameter uncertainty modeling of a macroscale hydrologic model. The Bayesian approach implemented using Markov Chain Monte Carlo (MCMC) methods is used in this study to model uncertainty arising from calibration parameters of the Variable Infiltration Capacity (VIC) MHM. The study examines large‐scale hydrologic impacts for Indian river basins and changes in discharges for three major river basins with distinct climatic and geographic characteristics, under climate change. Observed/reanalysis meteorological variables such as precipitation, temperature and wind speed are used to drive the VIC macroscale hydrologic model. An objective function describing the fit between observed and simulated discharges at four stations is used to compute the likelihood of the parameters. An MCMC approach using the Metropolis‐Hastings algorithm is used to update probability distributions of the parameters. For future hydrologic simulations, bias‐corrected GCM projections of climatic variables are used. The posterior distributions of VIC parameters are used for projection of 5th and 95th percentile discharge statistics at four stations, namely, Farakka, Jamtara, Garudeshwar, and Vijayawada for an ensemble of three GCMs and three scenarios, for two time slices. Spatial differences in uncertainty projections of runoff and evapotranspiration for years 2056–2065 for the a1b scenario at the 5th and 95th percentile levels are also projected. Results from the study show increased mean monthly discharges for Farakka and Vijayawada stations, and increased low, mid and high duration flows at Farakka, Jamtara and Vijayawada for the future. However, it is seen that uncertainty introduced due to choice of GCM, is larger than that due to parameter uncertainty for the VIC MHM. The largest effects of runoff predictive uncertainty due to uncertainty in VIC parameters are seen in the Himalayan foothills belt, and the high‐precipitation Northeast region of the country. It is demonstrated through the study that it is relevant and feasible to provide Bayesian uncertainty estimates for macroscale models in projection of large‐scale and regional hydrologic impacts.